A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$4.50$, and sales equaled $$42.00$ in total. There were $4$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+4.5y = 42}$ ${y = x+4}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+4}$ for $y$ in the first equation. ${7.5x + 4.5}{(x+4)}{= 42}$ Simplify and solve for $x$ $ 7.5x+4.5x + 18 = 42 $ $ 12x+18 = 42 $ $ 12x = 24 $ $ x = \dfrac{24}{12} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+4}$ to find $y$ ${y = }{(2)}{ + 4}$ ${y = 6}$ You can also plug ${x = 2}$ into $ {7.5x+4.5y = 42}$ and get the same answer for $y$ ${7.5}{(2)}{ + 4.5y = 42}$ ${y = 6}$ $2$ bags of candy and $6$ bags of cookies were sold.